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∫[(3x^4+2x^2)/(x^2-1)]dx=∫3x^2dx-∫dx+∫1/(x^2+1)dx请问这个是怎么变化的?
题目详情
∫[(3x^4+2x^2)/(x^2-1)]dx = ∫3x^2dx - ∫dx + ∫1/(x^2+1)dx 请问这个是怎么变化的?
▼优质解答
答案和解析
是不是(3x^4+2x²)/(x²+1)?
=(3x^4+3x²-x²)/(x²+1)
=3x²(x²+1)/(x²+1)-x²/(x²+1)
=3x²-x²/(x²+1)
=3x²-(x²+1-1)/(x²+1)
=3x²-[1-1/(x²+1)]
=3x²-1+1/(x²+1)
=(3x^4+3x²-x²)/(x²+1)
=3x²(x²+1)/(x²+1)-x²/(x²+1)
=3x²-x²/(x²+1)
=3x²-(x²+1-1)/(x²+1)
=3x²-[1-1/(x²+1)]
=3x²-1+1/(x²+1)
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